Logarithm Operator

Logarithm Notation Annoated

The logarithm operator is the inverse operation of exponential. The subscript number is the base of the logarithm and the expression is what is being operated on. The relationship with exponets can be expressed using the two equations below:

Examples

Base 2

By restricting the logarithm operator to base illustrates the pattern that the operator captures.

Base 3

Base 5

Properties of Logarithms

Name Property
Product
Quotient

Exponents, Logarithms and Radicals

The exponential operator is closely related to the logarithm and radical operators. For example, given the scenario of exponential population growth, the relationship between the three operators is expressed below. Note, in this hypothetical scenario the initial population is represented with the value of .

Equation Operator
Exponent
Given the growth rate and the time elapsed, the exponent operator returns the population.
Logarithm
Given the growth rate and the population the logarithm operator returns the time elapsed.
Radical
Given the time elapsed and the population the radical operator returns the growth rate.

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